A long chain of P-points

2016/07/25 by Borisa Kuzeljevic, Kuzeljevic, Borisa, Dilip Raghavan +1 · 2 citations
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.1607.07188

29 pages, submitted

arxiv created 2016/07/25 · arxiv updated 2016/07/26

Abstract

The notion of a δ-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each δ< ω₂, any δ-generic sequence of P-points can be extended to an ω₂-generic sequence. This shows that the Continuum Hypothesis implies that there is a chain of P-points of length \mathfrakc⁺ with respect to both Rudin-Keisler and Tukey reducibility. The proofs can be easily adapted to get such a chain of length \mathfrakc⁺ under a more general hypothesis like Martin's Axiom. These results answer an old question of Andreas Blass.

Cited by

• Chains of P-points
• On the Rudin-Blass Ordering of Measures

Related

• Chains of P-points
• On embedding certain partial orders into the P-points under RK and Tukey reducibility
• On Recurrence Axioms
• There may be exactly n Q-points
• Lower bounds of sets of P-points